A Solution to Goldbach’S Conjecture

Abhijit Manohar^1,

¹Kolhapur, Maharashtra, India

Cite this paper:
Abhijit Manohar. A Solution to Goldbach’S Conjecture. American Journal of Mathematical Analysis. 2025; 11(1):12-13. doi: 10.12691/ajma-11-1-1

Abstract

The discussion revisits Goldbach’s conjecture by outlining a numerical approach that expresses every even integer as the sum of two prime numbers through relationships based on the form 6k plus or minus 1. The analysis shows how pairs of constants can be used to generate corresponding primes for any even value by drawing on the structure of integers within modular classes. Examples from small values and extended ranges, including even numbers between 1000 and 1100, demonstrate how specific combinations of k and k' yield valid prime pairs. The argument is supported by broader computational work that has explored the conjecture up to very large magnitudes, reinforcing the view that even integers consistently align with prime pair representations within this framework.

Keywords:
Goldbach conjecture prime numbers LeonhardEuler even integers tested for 4 x 10¹⁸

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References:

[1]	In the printed version published by P. H. Fuss [1] 2 is misprinted as 1 in the marginal conjecture.
[2]	"Letter XLIV, Euler to Goldbach" (PDF). Correspondence of Leonhard Euler. Mathematical Association of America. 30 June 1742. Archived (PDF) from the original on 2024-09-17. Retrieved 2025-01-19.
[3]	Oliviera e Silva, Tomas; Herzog, Siegfried; Pardi, Silvio (July 2014). "Empirical Verification of the Even Goldbach Conjecture and Computation of up to 4 · 1018" (PDF). Mathematics of Computation. 83 (288). American Mathematical Society: 2033–2068. Archived (PDF) from the original on 15 June 2025. Retrieved 16 July 2025.